1.4.1 Agile development mode

We use the agile development mode we learned. At the beginning of the project, we discuss everyone’s previous disciplines and expertise and assign tasks. We set every two weeks as a sprint, and the whole project is divided into four sprints. Each sprint had a sprint planning meeting, sprint review meeting, and sprint retrospective meeting. In addition, we processed scrum daily meetings to monitor progress and solve problems.

1.4.2 Github

We established the Github repository to share our code and materials: Github link

The variable we used from the covid_full data set:

1. Location: Indicate the name of the country.

2. Date: Indicate the time.

3. Stringency_index: It represents the strict degree of government control. It is a composite measure based on 9 response indicators, rescaled to a value from 0 to 100 (100 = strictest response).

4. New_cases_per_million: It represents the new confirmed cases of COVID-19 per 1,000,000 people. The reason why we use new_cases_per_million is due to the total population of each country being different, this variable makes the comparison results to be more fair and accurate.

The variable we used from the oxford data set:

1. CountryName, Date, StringencyIndex: Same as the covid_full data set

2. C1-C8, H1: indicate the 9 response indicators of the stringency index including School closures, Workplace closures, Cancel public events, Restrictions on gatherings, Close public transport, Stay at home requirements, Restrictions on internal movement, International travel controls, and Public information campaigns respectively. The value means the strict level of the indicator.

4.1.1 Combined First Difference

Combined FD:

The first difference represents the difference between two consecutive adjacent terms. We use the first-order difference to view the changes between the data of two adjacent periods to observe the changes in stringency index and new cases.

#calculate the first difference of stringency_index
cleaned_covid$stringency_difference <- 0
most_diff <- data.frame()
max_stringency_diff <- c()
countr <- c()
for (i in countries){
  index <- which ( cleaned_covid$country == i )
  this_country <- cleaned_covid[ cleaned_covid$country == i , ]
  difference <- diff( this_country$stringency)
  temp_max <- max(difference,na.rm = TRUE)
  max_stringency_diff <- append(max_stringency_diff, temp_max)
  countr <- append(countr, i)
  temp_frame <- data.frame(countr,max_stringency_diff)
  most_diff <- rbind(most_diff, temp_frame)
  cleaned_covid[index, ]$stringency_difference <- c(0,   difference)
}

#calculate the first difference of total_new_cases_per_million
cleaned_covid$new_cases_difference  <- 0

for (i in countries){
  index <- which ( cleaned_covid$country == i )
  this_country <- cleaned_covid[ cleaned_covid$country == i , ]
  difference <- diff( this_country$total_new_cases_per_million)
  cleaned_covid[index, ]$new_cases_difference  <- c(0,   difference)
}

#combine the FD of stringency_index and total_new_cases_per_million
cleaned_covid$new_cases_difference<-cleaned_covid$new_cases_difference/100
p_6 <- ggplot(data = cleaned_covid) +geom_line(aes(x = time, y = new_cases_difference, color = "new_cases_difference"))+ geom_line(aes(x = time, y = stringency_difference, color = "stringency_difference")) + facet_wrap( ~ country, scale = "free_y") + labs(title="Figure 1: New Cases vs Stringency FD", x ="Time", y = "Value") + theme(
plot.title = element_text(color="#99CCFF", size=14, face="bold"),
axis.title.x = element_text(color="#66B2FF", size=14, face="bold"),
axis.title.y = element_text(color="#66B2FF", size=14, face="bold")
)+scale_x_date(breaks = "3 month",labels=date_format("%m"))+ theme(axis.text.x = element_text(angle = 45, hjust = 1))
plotly::ggplotly(p_6)

We combined the FD figures of stringency_index and total_new_cases_per_million and scaled the total_new_cases_per_million by dividing 100. Obviously, the countries with large fluctuations of stringency_index have a small total_new_cases_per_million changing range, such as Mexico, and the Philippines. On the contrary, relatively smooth changes of stringency_index have a relatively large change range of total_new_cases_per_million, like the United States and Spain.

Thus, it indicates that the government could adjust policies constantly based on the real-time situation to better control the new case and inflexible policies cannot control the epidemic.

4.1.2 Hierarchical Clustering

For further investigation, we use hierarchical clustering to assess grouping patterns. For clustering, Manhattan distance is used in both graphs. The Manhattan distance indicates the absolute wheelbase sum of two points in the standard coordinate system.

Before clustering, a distance matrix with a relative size of 20 X 20 was first created. Manhattan distance between each country was calculated using the Manhattan distance formula, and those with similar distances were classified into four categories in total. ggplot is then used to plot the country groups divided by the cluster.

Stringency Cluster:

# x is first time series, y is second time series
#manhattan distance calculation
manhattan_dist <-
  function(x, y, p){
    distance = sum((x - y), na.rm = TRUE)
    return(distance)
}

# Hierarchical clustering for stringency
options(warn = -1)
p = 2
covid_list = split.data.frame(cleaned_covid[,c("time","stringency")], cleaned_covid$country)
n = length(countries)
distance_matrix <- matrix(0, n, n)
dateindex = covid_list[[1]]$time
for (i in 1:n ){
    for (j in 1:n){
          index_i = match(covid_list[[i]]$time, dateindex)
          index_j = match(covid_list[[j]]$time, dateindex) 
          ts_i <- covid_list[[i]][index_i,"stringency"]
          ts_j <- covid_list[[j]][index_j,"stringency"]
          distance_matrix[i,j] <-  manhattan_dist(ts_i, ts_j, p)
    }
}
rownames(distance_matrix) <- colnames(distance_matrix) <- countries
distance_matrix[!is.finite(distance_matrix)] <- 0

matrix_dist <- as.dist(distance_matrix)
hclust_res <- hclust( matrix_dist, method = "ward.D")  
hclust_cluster <-
  cutree(hclust_res, k = 4) %>% as.factor %>% as.data.frame

# draw the line chart basd on the stringency cluster
cleaned_covid$cluster <-hclust_cluster[as.character(cleaned_covid$country), 1]

p_2 = ggplot() +
  geom_line(data =cleaned_covid, aes(x = time, y = stringency, color = country)) +
  facet_wrap( ~ cluster,scales = "fixed", ncol = 1) +
  theme_bw() + labs(title="Figure 2: Stringency Index Change Trend", x ="Time", y = "Stringency Index") + theme(
plot.title = element_text(color="#99CCFF", size=14, face="bold"),
axis.title.x = element_text(color="#66B2FF", size=14, face="bold"),
axis.title.y = element_text(color="#66B2FF", size=14, face="bold")
)
plotly::ggplotly(p_2)

As you can see from the stringency_index line chart, most countries maintained highly stringency_index until July 2021 and then began to decline slowly over time, such as France, Colombia, and Spain. For example, France announced in early July that masks would not be mandatory in nightclubs. In addition, children will be allowed to return to school when classes begin in September[1].

Some countries, such as Poland, the UK, and the US, had the highest levels of state control in January 2021. Policy controls in the UK dropped sharply around May, but after a ban on courses for almost a year, the change left almost all UK schools open by the end of May 2021, with stay-at-home orders lifted across the country in mid-April[2]. For the United States, the severity of the closure and containment indicators decreased in 2021, with the sharp decline in policy severity occurring in March 2021[3].

In addition, some countries, such as India and Mexico, are classified into one category due to relatively frequent fluctuations, indicating that the degree of policy control in these countries has been adjusted more times.

New Cases Cluster:

#scale the total_new_cases_per_million
library("scales")
trend <- cleaned_covid
trend$total_new_cases_per_million <- rescale(trend$total_new_cases_per_million, to = c(0, 1))

# Hierarchical clustering for total_new_cases_per_million
options(warn = -1)
p = 2
covid_list = split.data.frame(trend[,c("time","total_new_cases_per_million")], trend$country)
n = length(countries)
distance_matrix <- matrix(0, n, n)
dateindex = covid_list[[1]]$time
for (i in 1:n ){
    for (j in 1:n){
          index_i = match(covid_list[[i]]$time, dateindex)
          index_j = match(covid_list[[j]]$time, dateindex) 
          ts_i <- covid_list[[i]][index_i,"total_new_cases_per_million"]
          ts_j <- covid_list[[j]][index_j,"total_new_cases_per_million"]
          distance_matrix[i,j] <-  manhattan_dist(ts_i, ts_j, p)
    }
}
rownames(distance_matrix) <- colnames(distance_matrix) <- countries
distance_matrix[!is.finite(distance_matrix)] <- 0

matrix_dist <- as.dist(distance_matrix)
hclust_res <- hclust( matrix_dist, method = "ward.D")  
hclust_cluster <-
  cutree(hclust_res, k = 4) %>% as.factor %>% as.data.frame

#draw the line chart based on new cases cluster
trend$cluster <-hclust_cluster[as.character(trend$country), 1]

p_4 = ggplot() +
  geom_line(data =trend, aes(x = time, y = total_new_cases_per_million, color = country)) +
  facet_wrap( ~ cluster,scales = "fixed", ncol = 1) +
  theme_bw() + labs(title="Figure 3: New Cases Change Trend", x ="Time", y = "New Cases per Million") + theme(
plot.title = element_text(color="#99CCFF", size=14, face="bold"),
axis.title.x = element_text(color="#66B2FF", size=14, face="bold"),
axis.title.y = element_text(color="#66B2FF", size=14, face="bold")
)

plotly::ggplotly(p_4)

According to the clustering results of New Cases, the United States is divided into one category independently due to its large fluctuation within a year. Although some countries, such as the UK and Poland, still have cases grouped, the extent of the UK policy mentioned above shows that relevant restrictions will be lifted. While wearing masks is still mandatory, the number of new cases in the UK began to rise sharply in mid-May.

Although France remains a good example, it is grouped with India and Italy because of a more subdued increase in cases until August. On the other hand, France saw a sharp rise in new cases in August and continued to rise until January 2022, largely because of the lifting of restrictions after July.

By comparing the two cluster line charts, we can realize that the degree of policy control in each country is closely related to the increase of cases, and the loosening of policies is likely to lead to a rapid increase in cases. In addition, the United States was grouped with countries such as the United Kingdom in the first line chart but was separately classified in the case chart. This shows that although the policy of the United States is roughly the same as that of these countries, the policy of the United States is not very efficient compared with similar countries. Therefore, the audience (policymakers in each country) should not always learn the control policies of other countries but should start from their own country and formulate related policies according to the actual situation of their own country to change the degree of the policy control.

4.2.1 Map(lag time)

Lag time calculation:

The “lag time” is the difference between the time from the stringency_index starts to increase until the total_new_cases_per_million start to decrease and record the two dates as "start_date" and "end_date" of the lag time respectively, and calculated the differences between two dates represented in days. Furthermore, we compared the efficiency of policies in different counties by finding the longest lag time in each country and storing it in the lag_data data frame as “max lag time” with the corresponding country and start date.

#calculate the lag time of each country
lag_data <- data.frame()

id <- 1
for (i in 1:length(countries)) {
  lag_location = countries[i]
  lag_countries <- cleaned_covid %>% dplyr::filter(country == lag_location)
  start <- NULL
  start_date = NULL
  end_date = NULL
  max_lag_difftime = 0
  j = 1
  while (j < nrow(lag_countries)){
    temp_index <- lag_countries[j,]$stringency
    if(!is.na(temp_index)){
      if( j != nrow(lag_countries)){
        if (lag_countries[j,]$stringency < lag_countries[j+1,]$stringency) {
          start_date = lag_countries[j+1,]$time
          for (k in j+1:nrow(lag_countries)-1) {
            temp_case <- lag_countries[k,]$total_new_cases_per_million 
            temp_case_next <- lag_countries[k+1,]$total_new_cases_per_million
            if(!is.na(temp_case) && !is.na(temp_case_next) && length(temp_case) != 0 && length(temp_case_next) != 0){
              
              if (lag_countries[k,]$total_new_cases_per_million > lag_countries[k+1,]$total_new_cases_per_million) {
                end_date = lag_countries[k+1,]$time
                lag_difftime = difftime(end_date, start_date, units = "days")
                if (lag_difftime >= max_lag_difftime) {
                  max_lag_difftime = lag_difftime
                  start <- start_date
                }
                
                start_date = end_date
                j = k
                break
                
              }
            } else{
              break
            }
            
          }
          j = j + 1
        }
        
      }else{
        break
      }
    }else{
      break
    }
    j = j + 1
    
    
  }
  
  sub_lag_data <- data.frame(id,countries[i], max_lag_difftime, start)
  lag_data <- rbind(lag_data, sub_lag_data)
  id <- id + 1

}
names(lag_data)[2] <- "Country"

Lag Map:

#read the 2014_world_gdp_with_codes.csv and combine with the lag_data
word_geo <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/2014_world_gdp_with_codes.csv")

world_merge<- merge(word_geo, lag_data, 
                             by.x = "COUNTRY", by.y = "Country",
                             all.x = TRUE)

#use the national geographic location data in the word_geo and the lag value in lag_data to draw the map
world_map <- plot_ly(world_merge, type='choropleth', locations=world_merge$CODE, z=world_merge$max_lag_difftime, text=world_merge$COUNTRY, colorscale="RdBu")%>%layout(title = 'Figure 4: COVID19: The max lag time in different countries', font=t, plot_bgcolor = "#e5ecf6")

world_map

A geographic data was combined with the cleaned max lag time data to show the max lag time in different countries. The max lag time values ranging from small to large are represented by colors ranging from cool to warm (blue to red). From the map, there are several countries in orange and red on the map, such as Indonesia, the Philippines, and Iran, which indicates that these countries have a relatively large max lag time. In contrast, in South Africa, France, and Italy, they may use less than 40 days to decrease new cases after the stringency index increases.

This map shows that the policies may have effects on decreasing the number of total new cases, but the timing of the policies’ effects varies from country to country and different policies have different effects on the new cases.

4.2.2 Indicators Difference

The indicators difference represents the changed indicators in each country when the lag time is largest which means the policies changed.

For countries with states information, we choose the state with the highest average value to represent the change of the indicator in that country which is more representative.

#find the Indicators Difference of the max lag time in each country
policy <- data.frame()
for (i in 1:nrow(lag_data)){
  max_mean_row <- 1
  max_mean <- 0
  specific_date = lag_data[i,]$start
  specific_country = lag_data[i,]$Country
  single_data <- cleaned_oxford %>% dplyr::filter(time == specific_date,country == specific_country)
  for ( j in nrow(single_data)){
    cur_mean <- mean(unlist(single_data$elements_diff[[j]]))
    if(cur_mean > max_mean){
      max_mean <- cur_mean
      max_mean_row <- j
    }
  }
  theRow <- single_data$elements_diff[[max_mean_row]]
  temp <- data.frame(specific_country,theRow[1],theRow[2],theRow[3],theRow[4],theRow[5],theRow[6],theRow[7],theRow[8],theRow[9])
  policy <- rbind(policy, temp)
}

names(policy)[1] <- "Country Name"
names(policy)[2] <- "C1"
names(policy)[3] <- "C2"
names(policy)[4] <- "C3"
names(policy)[5] <- "C4"
names(policy)[6] <- "C5"
names(policy)[7] <- "C6"
names(policy)[8] <- "C7"
names(policy)[9] <- "C8"
names(policy)[10] <- "H1"


policy %>%
  kbl(caption = "Table 1: Indicators Difference") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"),fixed_thead = T)%>%kable_paper(full_width = F) %>%
  column_spec(1, bold = T, color = "white", background = "#1F456E")

By comparing the specific measures of the country stringency index above, those countries with shorter declines in new cases have imposed higher-level restrictions on the activities and venues for large-scale gatherings and movements of people. In addition, “Stay at home requirements” and “Restrictions on internal movement” can reduce the rise in infection rates even at relatively low levels, reducing new cases to a certain extent (Wibbens, Koo, & McGahan, 2020).

Our target audience may consider effective measures according to their own national conditions to promote the decline of new cases in their own countries.